{"paper":{"title":"A new new coproduct on quantum loop algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A coproduct is defined on general quantum loop algebras that reduces to the Drinfeld-Jimbo coproduct on U_q(ĝ).","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Andrei Negu\\c{t}","submitted_at":"2026-02-01T10:00:10Z","abstract_excerpt":"Quantum loop algebras generalize $U_q(\\widehat{\\mathfrak{g}})$ for simple Lie algebras $\\mathfrak{g}$, and they include examples such as quantum affinizations of Kac-Moody Lie algebras, K-theoretic Hall algebras of quivers, and BPS algebras for toric Calabi-Yau threefolds. In the present paper, we define a coproduct on general quantum loop algebras, which coincides with the Drinfeld-Jimbo coproduct in the particular case of $U_q(\\widehat{\\mathfrak{g}})$. We use our construction to prove fundamental facts about representations of quantum loop algebras, such as the rationality of $R$-matrices, m"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"we define a coproduct on general quantum loop algebras, which coincides with the Drinfeld-Jimbo coproduct in the particular case of U_q(ĝ)","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That a single coproduct can be defined on arbitrary quantum loop algebras while preserving all required algebraic compatibilities (coassociativity, compatibility with the algebra structure) that hold in the special case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new coproduct is defined on general quantum loop algebras that coincides with the Drinfeld-Jimbo coproduct for U_q(ĝ).","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A coproduct is defined on general quantum loop algebras that reduces to the Drinfeld-Jimbo coproduct on U_q(ĝ).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"15390bb0f7fb40713f8c71119ec67a3c58504740fdb2dc7ba77c93f0e21dfb19"},"source":{"id":"2602.01130","kind":"arxiv","version":3},"verdict":{"id":"88021937-d0cf-4979-9456-2493a945b293","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T08:44:43.438661Z","strongest_claim":"we define a coproduct on general quantum loop algebras, which coincides with the Drinfeld-Jimbo coproduct in the particular case of U_q(ĝ)","one_line_summary":"A new coproduct is defined on general quantum loop algebras that coincides with the Drinfeld-Jimbo coproduct for U_q(ĝ).","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That a single coproduct can be defined on arbitrary quantum loop algebras while preserving all required algebraic compatibilities (coassociativity, compatibility with the algebra structure) that hold in the special case.","pith_extraction_headline":"A coproduct is defined on general quantum loop algebras that reduces to the Drinfeld-Jimbo coproduct on U_q(ĝ)."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.01130/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}